Select the correct statements for a particle in a state of motion.

Options

A. If speed of the particle changes then velocity of the particle must change and it must have non-zero acceleration.
B. If velocity of the particle change then its speed must also change and particle must have non-zero acceleration.
C. When particle moves in a straight line with changing speed then its velocity may remain constant.
D. When velocity of the particle changes then its speed may or not change but particle must have some acceleration.

Answer

To solve the question regarding the correct statements for a particle in a state of motion, let's analyze each statement step by step.

### Step-by-Step Solution:

1. **Understanding Velocity and Speed:**
- Velocity is a vector quantity that includes both magnitude (speed) and direction.
- Speed is the magnitude of velocity and is a scalar quantity.

2. **Statement Analysis:**
- **Statement A:** "If the speed of a particle changes, then the velocity of the particle must also change."
- **Analysis:** This statement is true. If the speed (magnitude of velocity) changes, it directly implies that the velocity (which includes direction) must change as well.

3. **Statement B:** "If the velocity of the particle changes, then the speed of the particle must also change."
- **Analysis:** This statement is false. A particle can change its velocity by changing direction while maintaining the same speed (e.g., uniform circular motion). Therefore, the speed does not necessarily have to change when velocity changes.

4. **Statement C:** "When the particle moves in a straight line with a changing speed, then its velocity may remain constant."
- **Analysis:** This statement is false. If the speed is changing, the velocity must also change because velocity is dependent on both speed and direction. Thus, if speed changes, velocity cannot remain constant.

5. **Statement D:** "When the velocity of the particle changes, its speed may or may not change, but the particle must have some acceleration."
- **Analysis:** This statement is true. A particle can change its velocity while maintaining constant speed (as in circular motion), and if there is a change in velocity, there must be acceleration.

### Conclusion:
Based on the analysis:
- **Correct Statements:** A and D
- **Incorrect Statements:** B and C

### Final Answer:
The correct statements for a particle in a state of motion are A and D.